Question

You are the owner of a high-end shoe factory called Rike. There are no barriers to entry in the shoe market. But not only that: you realized that while you were attending online lecture last week you shared your shoe building process with everyone in the class. The people you once thought of as friends could now turn into your greatest enemies. It’s a bummer, but those are part of the risks of online lectures.

Luckily your favorite economics class has proven useful once again and has enlightened you with the following information to guide your business decisions:

Q （demand）=2,500–5P

Q（supply）=95P

TC=4Q^2 -15Q+76

Where QD is the total market demand for shoes, QS the total market supply for shoes, TC your

firm’s total cost function.

A. (10 points) Find the market equilibrium price and quantity. Graphically illustrate the equilibrium.

B. (15 points) Find the output your firm supplies and the total profit/loss you make. On a new graph below illustrate both the equilibrium and profit/loss you make.

C. (10 points) Find the number of firms that are active in the industry at market equilibrium.

D. (10 points) Calculate the price below which you will not produce any output in the long-run.

Answer 1

Solution:

Given data

Market demand:

Market supply:

a)

Market equilibrium occurs at the intersection point of market demand and market supply i.e,

Market equilibrium price is 25.

and

Market equilibrium quantity is 2375.

b) A perfectly competitive firm produce at

( firm marginal cost function)

Each firm will supply 5 units in equilibrium.

Profit of each form:

Each form will earn a profit in equilibrium

Shaded region = profit

c)

market equilibrium quantity = 2375

each firm equilibrium quantity = 5

All firms in perfectly competitive market are same,

i.e, number of firms

Number of firms = 475

There are 475 firms active in industry at market equilibrium.

d)

Inlong run a perfectly competive firm will not produce it price is less than minimum value of ATC (i.e, minimum value of average total cost)

intersects ATC at its minimum point

Set  

is minimum

put in ATC

Minimum value of ATC is 19.87

Hence in log run firm will not produce any output if price is below 19.87.

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